Forward Elastic Scattering of Light on Light, γ+γ\toγ+γ

Abstract

The forward elastic scattering of light on light, {\em i.e.,} the reaction $γ+γ\to γ+γ$ in the forward direction, is analyzed utilizing real analytic amplitudes. We calculate $ρ_{γγ}$, the ratio of the real to the imaginary portion of the forward scattering amplitude, by fitting the total $γγ$ cross section data in the high energy region $5 GeV \le \sqrt s \le 130 $ GeV, assuming a cross section that rises asymptotically as $\ln^2 s$. We then compare $ρ_{γγ}$ to $ρ_{nn}$, the ratio of the even portions of the $pp$ and $\pbar p$ forward scattering amplitudes, as well as to $ρ_{γp}$, the $ρ$ value for Compton scattering. Within errors, we find that the three $ρ$-values in the c.m.s. energy region $5 GeV \le \sqrt s \le 130$ GeV are the same, as predicted by a factorization theorem of Block and Kadailov.